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Announcements

Announcements. Project 3 extension: Wednesday at noon Final project proposal extension: Friday at noon consult with Steve, Rick, and/or Ian now! Project 2 artifact winners. Readings

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Announcements

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  1. Announcements • Project 3 extension: Wednesday at noon • Final project proposal extension: Friday at noon • consult with Steve, Rick, and/or Ian now! • Project 2 artifact winners... • Readings • S. M. Seitz and C. R. Dyer, Photorealistic Scene Reconstruction by Voxel Coloring, International Journal of Computer Vision, 35(2), 1999, pp. 151-173. • http://www.cs.washington.edu/homes/seitz/papers/ijcv99.pdf

  2. camera 1 camera 1 projector projector camera 2 Active stereo with structured light • Project “structured” light patterns onto the object • simplifies the correspondence problem Li Zhang’s one-shot stereo

  3. Active stereo with structured light

  4. Laser scanning • Optical triangulation • Project a single stripe of laser light • Scan it across the surface of the object • This is a very precise version of structured light scanning • Digital Michelangelo Project • http://graphics.stanford.edu/projects/mich/

  5. 3D cameras Portable 3D laser scanner (this one by Minolta)

  6. Multiview stereo

  7. Choosing the stereo baseline • What’s the optimal baseline? • Too small: large depth error • Too large: difficult search problem all of these points project to the same pair of pixels width of a pixel Large Baseline Small Baseline

  8. The Effect of Baseline on Depth Estimation

  9. 1/z width of a pixel width of a pixel pixel matching score 1/z

  10. Multibaseline Stereo • Basic Approach • Choose a reference view • Use your favorite stereo algorithm BUT • replace two-view SSD with SSD over all baselines • Limitations • Must choose a reference view (bad) • Visibility! • CMU’s 3D Room Video

  11. Known Scene Unknown Scene • Forward Visibility • known scene • Inverse Visibility • known images The visibility problem • Which points are visible in which images?

  12. Volumetric stereo Scene Volume V Input Images (Calibrated) Goal: Determine occupancy, “color” of points in V

  13. Discrete formulation: Voxel Coloring Discretized Scene Volume Input Images (Calibrated) • Goal: Assign RGBA values to voxels in V • photo-consistent with images

  14. True Scene All Scenes (CN3) Photo-Consistent Scenes Complexity and computability Discretized Scene Volume 3 N voxels C colors

  15. Issues • Theoretical Questions • Identify class of all photo-consistent scenes • Practical Questions • How do we compute photo-consistent models?

  16. Voxel coloring solutions • 1. C=2 (shape from silhouettes) • Volume intersection [Baumgart 1974] • For more info: Rapid octree construction from image sequences. R. Szeliski, CVGIP: Image Understanding, 58(1):23-32, July 1993. (this paper is apparently not available online) or • W. Matusik, C. Buehler, R. Raskar, L. McMillan, and S. J. Gortler, Image-Based Visual Hulls, SIGGRAPH 2000 ( pdf 1.6 MB ) • 2. C unconstrained, viewpoint constraints • Voxel coloring algorithm [Seitz & Dyer 97] • 3. General Case • Space carving [Kutulakos & Seitz 98]

  17. Reconstruction from Silhouettes (C = 2) Binary Images • Approach: • Backproject each silhouette • Intersect backprojected volumes

  18. Volume intersection • Reconstruction Contains the True Scene • But is generally not the same • In the limit (all views) get visual hull • Complement of all lines that don’t intersect S

  19. Voxel algorithm for volume intersection • Color voxel black if on silhouette in every image • for M images, N3 voxels • Don’t have to search 2N3 possible scenes! O( ? ),

  20. Properties of Volume Intersection • Pros • Easy to implement, fast • Accelerated via octrees [Szeliski 1993] or interval techniques [Matusik 2000] • Cons • No concavities • Reconstruction is not photo-consistent • Requires identification of silhouettes

  21. Voxel Coloring Solutions • 1. C=2 (silhouettes) • Volume intersection [Baumgart 1974] • 2. C unconstrained, viewpoint constraints • Voxel coloring algorithm [Seitz & Dyer 97] • For more info: http://www.cs.washington.edu/homes/seitz/papers/ijcv99.pdf • 3. General Case • Space carving [Kutulakos & Seitz 98]

  22. 1. Choose voxel • Color if consistent • (standard deviation of pixel • colors below threshold) 2. Project and correlate Voxel Coloring Approach Visibility Problem: in which images is each voxel visible?

  23. Layers Depth Ordering: visit occluders first! Scene Traversal Condition: depth order is the same for all input views

  24. Panoramic Depth Ordering • Cameras oriented in many different directions • Planar depth ordering does not apply

  25. Panoramic Depth Ordering Layers radiate outwards from cameras

  26. Panoramic Layering Layers radiate outwards from cameras

  27. Panoramic Layering Layers radiate outwards from cameras

  28. Inward-Looking • cameras above scene • Outward-Looking • cameras inside scene Compatible Camera Configurations • Depth-Order Constraint • Scene outside convex hull of camera centers

  29. Calibrated Image Acquisition • Calibrated Turntable • 360° rotation (21 images) Selected Dinosaur Images Selected Flower Images

  30. Voxel Coloring Results (Video) Dinosaur Reconstruction 72 K voxels colored 7.6 M voxels tested 7 min. to compute on a 250MHz SGI Flower Reconstruction 70 K voxels colored 7.6 M voxels tested 7 min. to compute on a 250MHz SGI

  31. Limitations of Depth Ordering • A view-independent depth order may not exist p q • Need more powerful general-case algorithms • Unconstrained camera positions • Unconstrained scene geometry/topology

  32. Voxel Coloring Solutions • 1. C=2 (silhouettes) • Volume intersection [Baumgart 1974] • 2. C unconstrained, viewpoint constraints • Voxel coloring algorithm [Seitz & Dyer 97] • 3. General Case • Space carving [Kutulakos & Seitz 98] • For more info: http://www.cs.washington.edu/homes/seitz/papers/kutu-ijcv00.pdf

  33. Initialize to a volume V containing the true scene • Choose a voxel on the current surface • Project to visible input images • Carve if not photo-consistent • Repeat until convergence Space Carving Algorithm • Space Carving Algorithm Image 1 Image N …...

  34. V Photo Hull Which shape do you get? • The Photo Hull is the UNION of all photo-consistent scenes in V • It is a photo-consistent scene reconstruction • Tightest possible bound on the true scene V True Scene

  35. Space Carving Algorithm • The Basic Algorithm is Unwieldy • Complex update procedure • Alternative: Multi-Pass Plane Sweep • Efficient, can use texture-mapping hardware • Converges quickly in practice • Easy to implement Results Algorithm

  36. Multi-Pass Plane Sweep • Sweep plane in each of 6 principle directions • Consider cameras on only one side of plane • Repeat until convergence True Scene Reconstruction

  37. Multi-Pass Plane Sweep • Sweep plane in each of 6 principle directions • Consider cameras on only one side of plane • Repeat until convergence

  38. Multi-Pass Plane Sweep • Sweep plane in each of 6 principle directions • Consider cameras on only one side of plane • Repeat until convergence

  39. Multi-Pass Plane Sweep • Sweep plane in each of 6 principle directions • Consider cameras on only one side of plane • Repeat until convergence

  40. Multi-Pass Plane Sweep • Sweep plane in each of 6 principle directions • Consider cameras on only one side of plane • Repeat until convergence

  41. Multi-Pass Plane Sweep • Sweep plane in each of 6 principle directions • Consider cameras on only one side of plane • Repeat until convergence

  42. Space Carving Results: African Violet Input Image (1 of 45) Reconstruction Reconstruction Reconstruction

  43. Space Carving Results: Hand Input Image (1 of 100) Views of Reconstruction

  44. Properties of Space Carving • Pros • Voxel coloring version is easy to implement, fast • Photo-consistent results • No smoothness prior • Cons • Bulging • No smoothness prior

  45. Alternatives to space carving • Optimizing space carving • recent surveys • Slabaugh et al., 2001 • Dyer et al., 2001 • many others... • Graph cuts • Kolmogorov & Zabih • Level sets • introduce smoothness term • surface represented as an implicit function in 3D volume • optimize by solving PDE’s

  46. Alternatives to space carving • Optimizing space carving • recent surveys • Slabaugh et al., 2001 • Dyer et al., 2001 • many others... • Graph cuts • Ramin Zabih’s lecture • Level sets • introduce smoothness term • surface represented as an implicit function in 3D volume • optimize by solving PDE’s

  47. Level sets vs. space carving • Advantages of level sets • optimizes consistency with images + smoothness term • excellent results for smooth things • does not require as many images • Advantages of space carving • much simpler to implement • runs faster (orders of magnitude) • works better for thin structures, discontinuities • For more info on level set stereo: • Renaud Keriven’s page: • http://cermics.enpc.fr/~keriven/stereo.html

  48. Current/Future Trends • Optimizing with visibility • Kolmogorov & Zabih

  49. Current/Future Trends • Real-time algorithms • e.g., Buehler et al., image-based visual hulls, SIGGRAPH 2000

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